Bethe subalgebras of the group algebra of the symmetric group

Abstract

We introduce families of maximal commutative subalgebras, called Bethe subalgebras, of the group algebra of the symmetric group. Bethe subalgebras are deformations of the Gelfand-Zetlin subalgebra. We describe various properties of Bethe subalgebras.

AmsLaTeX, 32 pages; references updated

References in corpus (4)

• Opers with irregular singularity and spectra of the shift of argument subalgebra
• Quantization of the Gaudin System
• Limits of Gaudin algebras, quantization of bending flows, Jucys--Murphy elements and Gelfand--Tsetlin bases
• Gaudin Hamiltonians generate the Bethe algebra of a tensor power of vector representation of gl_N

Cited by in corpus (3)

• Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra
• Bethe subalgebras in Hecke algebra and Gaudin models
• Markov traces on affine and cyclotomic Yokonuma-Hecke algebras